Systems and methods for time-series data processing in machine learning systems

Abstract

Embodiments described herein provide using a measure of distance between time-series data sequences referred to as optimal transport warping (OTW). Measuring the OTW distance between unbalanced sequences (sequences with different sums of their values) may be accomplished by including an unbalanced mass cost. The OTW computation may be performed using cumulative sums over local windows. Further, embodiments herein describe methods for dealing with time-series data with negative values. Sequences may be split into positive and negative components before determining the OTW distance. A smoothing function may also be applied to the OTW measurement allowing for a gradient to be calculated. The OTW distance may be used in machine learning tasks such as clustering and classification. An OTW measurement may also be used as an input layer to a neural network.

What is claimed is: 
     
         1 . A method for measuring time-series data, the method comprising:
 receiving a first set of time-series data corresponding to a first system status variable over a first period of time;   receiving a second set of time-series data corresponding to a second system status variable over a second period of time;   determining a distance measurement between the first set and a second set, the determining comprising:
 summing a plurality of absolute values of differences of cumulative sums of the first set and the second set to provide the distance measurement; and 
 modifying the distance measurement with an unbalanced mass cost computed based on a difference between a first sum of values in the first set and a second sum of values in the second set; and 
   executing a control command pertaining to the first system status variable or the second system status variable based on the distance measurement.   
     
     
         2 . The method of  claim 1 , wherein:
 the cumulative sums of the first set and the second set are partial cumulative sums with a predetermined window size,   the first sum of values in the first set is a sum of a first subset of the values in the first set, and   the second sum of values in the second set is a sum of a second subset of the values in the second set.   
     
     
         3 . The method of  claim 1 , wherein the plurality of absolute values are smoothed approximations of absolute values. 
     
     
         4 . The method of  claim 3 , wherein:
 the second set of time series data is comprised of trainable parameters,   the distance measurement is input to a neural network, and   the executing the control command is further based on an output of the neural network.   
     
     
         5 . The method of  claim 1 , wherein at least one of the first set or the second set contains positive and negative values. 
     
     
         6 . The method of  claim 5 , further comprising:
 in response to determining that the first set or the second set contains both positive and negative values, splitting the first set into a first subset of all positive values and a second subset of all negative values and the second set into a third subset of all positive values and a fourth subset of all negative values;   wherein determining the distance measurement comprises determining a first distance measurement between the first and third subsets and determining a second distance measurement between the second and third subsets.   
     
     
         7 . The method of  claim 1 , further comprising:
 associating the first set with a class of time-series data based on the distance measurement.   
     
     
         8 . The method of  claim 1 , further comprising:
 associating the first set and the second set together in a cluster of time-series data sets based on the distance measurement.   
     
     
         9 . A system for measuring time-series data, the system comprising:
 a memory that stores a plurality of processor executable instructions;   a communication interface that receives a first set of time-series data corresponding to a first system status variable over a first period of time; and   one or more hardware processors that read and execute the plurality of processor-executable instructions from the memory to perform operations comprising:
 receiving a second set of time-series data corresponding to a second system status variable over a second period of time; 
 in response to determining that the first set or the second set contains both positive and negative values, splitting the first set into a first subset of all positive values and a second subset of all negative values and the second set into a third subset of all positive values and a fourth subset of all negative values; 
 summing a plurality of absolute values of differences of cumulative sums of the first subset and the third subset to provide a first distance measurement; 
 summing a plurality of absolute values of differences of cumulative sums of the second subset and the fourth subset to provide a second distance measurement; 
 adding the first distance measurement and the second distance measurement to provide a composite distance measurement; and 
 executing a control command pertaining to the first system status variable or the second system status variable based on the composite distance measurement. 
   
     
     
         10 . The system of  claim 9 , wherein the operations further comprise:
 modifying the composite distance measurement with an unbalanced mass cost computed based on a difference between a first sum of values in the first set and a second sum of values in the second set.   
     
     
         11 . The system of  claim 9 , wherein the cumulative sums of the first, second, and third subsets are partial cumulative sums with a predetermined window size. 
     
     
         12 . The system of  claim 9 , wherein:
 the plurality of absolute values of differences of cumulative sums of the first subset and the third subset are smoothed approximations of absolute values, and   the plurality of absolute values of differences of cumulative sums of the second subset and the fourth subset are smoothed approximations of absolute values.   
     
     
         13 . The system of  claim 12 , wherein:
 the second set of time series data is comprised of trainable parameters,   the composite distance measurement is input to a neural network, and   the executing the control command is further based on an output of the neural network.   
     
     
         14 . The system of  claim 9 , wherein the operations further comprise:
 associating the first set with a class of time-series data based on the composite distance measurement.   
     
     
         15 . The system of  claim 9 , wherein the operations further comprise:
 associating the first set and the second set together in a cluster of time-series data sets based on the composite distance measurement.   
     
     
         16 . A non-transitory machine-readable medium comprising a plurality of machine-executable instructions which, when executed by one or more processors, are adapted to cause the one or more processors to perform operations comprising:
 receiving a first set of time-series data corresponding to a first system status variable over a first period of time;   receiving a second set of time-series data corresponding to a second system status variable over a second period of time;   determining a distance measurement between the first set and a second set, the determining comprising:
 summing a plurality of absolute values of differences of cumulative sums of the first set and the second set to provide the distance measurement; and 
 modifying the distance measurement with an unbalanced mass cost computed based on a difference between a first sum of values in the first set and a second sum of values in the second set; and 
   executing a control command pertaining to the first system status variable or the second system status variable based on the distance measurement.   
     
     
         17 . The non-transitory machine-readable medium of  claim 16 , wherein:
 the cumulative sums of the first set and the second set are partial cumulative sums with a predetermined window size,   the first sum of values in the first set is a sum of a first subset of the values in the first set, and   the second sum of values in the second set is a sum of a second subset of the values in the second set.   
     
     
         18 . The non-transitory machine-readable medium of  claim 16 , wherein the plurality of absolute values are smoothed approximations of absolute values. 
     
     
         19 . The non-transitory machine-readable medium of  claim 18 , wherein:
 the second set of time series data is comprised of trainable parameters,   the distance measurement is input to a neural network, and   the executing the control command is further based on an output of the neural network.   
     
     
         20 . The non-transitory machine-readable medium of  claim 16 , wherein at least one of the first set or the second set contains positive and negative values.